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arXiv 1107.2372math.OAmath.FA
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Hilbert C ~*-模中正则算子的局部整体原理

A local global principle for regular operators in Hilbert C*-modules

Jens Kaad, Matthias Lesch

摘要:

希尔伯特C*-模是希尔伯特空间的类似物,其中C* 代数扮演标量场的角色。随着卡斯帕罗夫的著名KK理论的出现,它们成为算子代数理论的标准工具。虽然希尔伯特C*-模的基本性质基本上可以平行于希尔伯特空间理论导出,但由于缺乏类似的投影定理,很快就导致了严重的障碍和困难。特别是无界算子理论是出了名的复杂,由于额外的规则性公理,这是不容易检查。本文利用无界算子的希尔伯特空间局部化给出了一个新的正则性判据。我们讨论了几个例子表明,该标准可以很容易地检查,它会导致非平凡的正则性结果。

英文摘要:

Hilbert C*-modules are the analogues of Hilbert spaces where a C*-algebra plays the role of the scalar field. With the advent of Kasparov's celebrated KK-theory they became a standard tool in the theory of operator algebras. While the elementary properties of Hilbert C*-modules can be derived basically in parallel to Hilbert space theory the lack of an analogue of the Projection Theorem soon leads to serious obstructions and difficulties. In particular the theory of unbounded operators is notoriously more complicated due to the additional axiom of regularity which is not easy to check. In this paper we present a new criterion for regularity in terms of the Hilbert space localizations of an unbounded operator. We discuss several examples which show that the criterion can easily be checked and that it leads to nontrivial regularity results.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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